Research on mathematical knowledge for teaching, and the relationships between subject matter knowledge (SMK) and pedagogic content knowledge (PCK), have been and continue to be of great interest across the world, not least because of the decreasing take-up of higher levels of mathematics study by school and university students in many countries. In this study we report on a novel approach to SMK and PCK through a focus on a CPD course running in two UK Universities within which what we call Big Ideas is a defining feature. Research findings from work at one of the Universities, consisting of a qualitative analysis of teachers' diary-writing feedback, video analysis of elements of the interactions during seminars, and developing dialogue between tutors and participants, suggest that the ‘Big Ideas’ notion has acted as a mediating artefact, opening up new ways for our teachers to induct students into mathematical thinking and at the same time develop their own mathematical knowledge and pedagogical knowledge; parallel development is noted amongst tutors. The methodology builds on that of the QUANTUM project in South Africa whereby teachers take part in critical analysis of pedagogy exemplified by tutors in interaction with theoretical considerations from research literature.